Visualization Study of Two-layer Reverse Roll Transfer

Abstract

Reverse roll coating in which a thin single layer of liquid is applied onto a substrate has been used in industry for decades and has been extensively analyzed in the literature. Modern coatings, however, are often composed of more than one layer to improve product performance and to reduce manufacturing cost. Pre-metered methods such as slot, slide and curtain coating are typically used to produce such multilayer coatings. If the caliper of the substrate to be coated is not constant, the coating gap and consequently the final film thickness deposited on the web will also be non-uniform. In this study we focused on the use of reverse roll technique with slot die liquid delivery system to produce a uniform thin two-layer coating. The use of this coating technique to produce such a coating has not been previously explored. The liquid film surface as it is transferred from a rigid steel roll to a deformable urethane covered roll was visualized in order to find out how the uniformity of two layer coating is affected by the speed ratio between two rolls, layers wet thickness and liquid viscosities. The effect of these parameters on the ribbing frequency and amplitude was also investigated.

The results show that in two layer coating, as in the single layer reverse transfer, there is a critical web speed above which ribbing occurs. The critical speed is determined by the bottom layer viscosity.

1. Introduction

In recent years, demand for special surface-treated steel sheets with a corrosion resistance function has expanded. Roll coating is widely used to coat a thin liquid layer onto a moving substrate. In this process, the liquid layer is taken up from a container and applied to the substrate after controlling the wet thickness. Multiple rolls are usually used in this process. A metered liquid layer is created in the gap between a pair of co-rotating (reverse roll) or counter-rotating (forward roll) cylinders. In order to obtain a uniform coating appearance in this process, it is necessary to clarify the flow states between the rolls. Many publications discussing single-layer roll coating processes are available.

In the case of forward roll coating, these studies have focused on the coating defect called ribbing, which is caused by the rotating motion of the rolls, and concluded that the operability limits could be shown by using a dimensionless number (Ca number).^1,2,3,4,5,6) In the case of reverse roll coating, experimental and analytical approaches are used to clarify the effects of the roll speed, liquid properties and roll gap on coating defects.^{7,8,9,10,11,12,13)}

Industrial products often require more than one layer for optimal performance. The most efficient way to manufacture these products is by coating all the layers at once before they are solidified. Multilayer films are usually produced by pre-metered methods such as slot, tensioned-web-over-slot die (TWOSD), slide and curtain coating techniques.^{14,15,16,17,18)}

Pre-metered multilayer coating is a complex process, as the flow is subjected to different flow instabilities and micro vortices that may compromise the quality of the final product.

If the caliper of the substrate to be coated is not constant, the coating gap and consequently the final film thickness deposited on the web will also be non-uniform. When the final product uniformity requirement is not a limiting factor, these drawbacks of precision multilayer coating can be avoided by coating two liquid layers onto an applicator roll using two layer slot coating and transferring the coating to the substrate in a reverse roll transfer process. However, in order to implement this approach in an industrial line, it is important to determine the set of conditions and liquid properties under which the transfer film remains uniform. To our knowledge, no systematic study of these conditions has been reported in the literature. This is the main goal of the present work.

2. Experimental Set-up and Procedure

The coating apparatus used for visualization of two-layer coating is shown in Fig. 1 and consisted of a two-layer slot die, a metal roll as the pickup roll, a deformable urethane-covered roll as the applicator roll, two precision gear pumps, two filters, two debubblers and two storage tanks with the appropriate tubing connecting the system. The bottom roll was rigidly mounted, and the top roll position was adjustable. The bottom roll was 4 inches in diameter. The top roll was 7 inches in diameter and was rubber-covered.

Fig. 1.

Sketch of coating apparatus.

A small 4 inch wide slot die, shown in Fig. 2, was sufficiently wide for a two-dimensional flow to develop away from its edges and was also easy to handle in laboratory scale experiments. The die was composed of three blocks. Shims of the desired thicknesses were placed between each pair of blocks to form feed slots of fixed height. A vacuum box was attached to the upstream block and connected to a vacuum pump. A low level vacuum was applied to the coating bead to produce a stable two-layer coating on the pickup roll. The direction of roll rotation used a reverse method to turn in the opposite direction between rolls. The coating liquid was supplied from the slot die to the bottom roll in a uniform state, passed the meniscus region and was then transferred to the top roll.

Fig. 2.

Detail of the two layer slot coating die with vacuum box and side plates removed.

Squeegees positioned on the opposite side from the liquid feed were used to remove the liquid from the rolls. The scrapped liquid was collected in order to measure the thickness of the film on each of the rolls. As a liquid presence on the metal pickup roll was not detected by squeegeeing, virtually 100% of the liquid film was transferred from the bottom roll to the top roll.

Glycerine-water solutions were used as the coating liquids. The viscosity of the solution was adjusted by dilution with water.

In this study, the liquid film surface as it is transferred from a slot die to the bottom roll and the meniscus between the two rolls were visualized in order to investigate how the uniformity of two-layer coating is affected by the speed ratio between the two rolls, the wet thicknesses of the layers and the viscosities of the liquids. Table 1 shows the experimental conditions of the study. The range of roll speeds was from 30 mpm to 120 mpm, and the range of viscosities for both layers was from 5×10^–3 Pa·s to 20×10^–3 Pa·s. The range of the wet thickness to the slot gap ratio (h/H) was from 0.1 to 0.7, where h is the wet thickness of each layer, and H is the distance between the slot die and the metal roll. The wet thickness of each layer was controlled by the pump flow rate and roll speed.

Table 1. Experimental condition.

Top roll speed [mpm]	30–120
Bottom roll speed [mpm]	30
Viscosity [Pa·s]	5×10–3 – 20×10–3
Gap (between die and metal roll) [μm]	50
Wet thickness/GAP [–]	0.1–0.7

A high speed camera (Photron FASTCAM-ultima APX) and high resolution camera (Imaging Source model DFK 31 BF03H) were used for visualization. The camera was positioned as indicated in Fig. 1 to visualize the liquid film as it was transferred from the bottom roll to the top roll. To make the flow visible, a fluorescent dye (Fluorescein disodium salt, 2-hydrate (green, which was dissolved in the coating the coating solution) was injected inside the bottom layer distribution chamber of the die. Figure 3 shows the dye injection schematic. A small hole was drilled through the side plate of the slot die in which the dye injection needle was placed. The dye concentration was approximately 1.0 wt%. The dye flow rate was controlled by a syringe pump and varied from 0.03 to 0.2 ml/min. A very small amount of dye was used, which was sufficient to visualize the line created by the dye without disturbing the original flow.

Fig. 3.

Die injection schematic.

Figure 4 shows a snapshot of the meniscus between the top and bottom rolls. This picture was taken by the high-speed camera at 250 frames per second. The meniscus region is defined by the continuous and dotted lines in the picture. The lower part of the picture is the bottom metal roll and the upper part is the top rubber-covered roll. The coating liquid was supplied from the coating die to the bottom roll and then transferred to the top roll. The roll speed of the top and bottom rolls was 30 mpm. The wet thickness ratios (h/H) of the top and bottom layers were 0.2 and 0.6, respectively. The small white spots in the figure located in the transfer meniscus were small bubbles present in the liquid, which were entrapped in the recirculation that appeared attached to the free surfaces under some conditions. Although the visualization region of this experiment was very narrow and visualization between the rolls was difficult by using only the tracer particles from one side, the existence of the small bubbles was very useful for visualization of the flow between the two rolls.

Fig. 4.

Example of high speed camera picture.

3. Results and Discussion

3.1. Flow State between Slot Die and Bottom Roll

Before visualizing the liquid transfer between the rolls, the conditions for uniform simultaneous coating between the slot die and bottom roll were investigated. The speed of the top and bottom rolls was 30 mpm, the viscosities of both layers were from 5×10^–3 Pa·s and the wet thickness was varied. Figure 5 shows the appearances of the coatings. The horizontal axis is the ratio of the bottom layer wet thickness and slot gap (h_bottom/H). The vertical axis is the ratio of the top layer wet thickness and slot gap (h_top/H).

Fig. 5.

Coating window between Die and bottom roll.

When the wet thickness of both layers was low, coating defects called air fingers occurred. The coating condition became uniform when the wet thickness was increased. However, when the wet thickness was increased further, for example, to h_bottom/H > 0.5, h_top/H > 0.4, leakage occurred from the upstream side of the slot die.

Figure 6 shows the effect of top layer viscosity. It was found that the uniform coating region became narrower when the top layer wet thickness was increased. These results clarified the conditions for uniform coating between the slot die and bottom roll. The experiment concerning liquid transfer between two rolls was conducted by using this coating condition.

Fig. 6.

Coating window between Die and bottom roll. (the effect of top layer viscosity).

3.2. Flow State of Meniscus between Two Rolls

Figure 7 shows snapshots of the transfer meniscus at different top roll speeds. The bottom roll speed was kept constant at 30 mpm, while the top roll speed was varied from 30 mpm to 80 mpm. The time interval between each image was 0.004 s. As in Fig. 4, the solid line in Fig. 7 shows the top of the meniscus, and the dotted line shows its bottom. At a speed ratio of 1.0; i.e., V_top=V_bottom=30 mpm, the meniscus is large and the movement of the bubbles clearly shows the recirculation attached to the free surface. As the top roll speed is raised, the viscous forces become stronger and the free surface moves toward the gap leading to a small meniscus region, as it is clear from Fig. 7(b). Recirculation is still present at V_top=60 mpm, but at V_top=80 mpm, the meniscus is small and recirculation has vanished, as shown in Fig. 7(c).

Fig. 7.

High speed camera pictures (meniscus region). (a) V_top=30 mpm, V_bottom=30 mpm (b) V_top=60 mpm, V_bottom=30 mpm (c) V_top=80 mpm, V_bottom=30 mpm (Top and bottom layer 5×10^–3 Pa·s, h_top/H=0.2, h_bottom/H=0.2).

When the top and bottom roll speeds were 30 mpm, the diameter of the recirculation was half the length of the meniscus. When the top roll speed was increased to 60 mpm, the meniscus was drawn into the contact point due to the expansion of the coating liquid caused by the velocity difference between the rolls. From this result, it is thought that the length of the meniscus decreased.

The evolution of the meniscus configuration as the top roll speed is raised is shown schematically in Fig. 8. This experiment clarified the fact that the recirculation became smaller or varnished when the speed ratio was increased because the position of the meniscus was transferred to the contact point of the rolls by the expansion of the liquid.

Fig. 8.

Outline of the flow between 2 rolls.

3.3. Results of Liquid Transfer between Two Rolls

The onset of ribbing can be determined by observing the streaklines formed by the injected dye at different top to bottom roll speed ratio, as shown in Fig. 9. The viscosities of the top and bottom layers were 20×10^–3 Pa·s and 5×10^–3 Pa·s, respectively. The ratios of the wet thickness and gap of the two rolls were h_top/H=0.4 and h_bottom/H>0.4, respectively. The speed of the bottom roll was kept constant at 30 mpm. The flow rate from the dye injection syringe was adjusted so that the fluorescent dye band was about 0.6 mm wide on the bottom roll. The lower part of the picture shows the bottom roll, the central part shows the transfer meniscus region and the upper part shows the top roll. The coating liquid moves from the bottom roll to the coating bead and is then transferred to the top roll. When the speed ratio between two rolls was below 3.46, the streakline was straight without variation in width, indicating a two-dimensional flow. At speed ratios above 3.69, the dye streakline width on the top roll increased, indicating a three-dimensional flow, i.e., the presence of ribbing. The movement of the coating liquid from the roll at the bottom to the top roll was almost uniform in the stage before ribbing, and with the generation of ribbing, the results confirmed diffusion in the width direction along the ruggedness of the ribbing.

Fig. 9.

Visualization of tracer movement.

The onset of the three-dimensional pattern can be determined by tracking the streakline width ratio, defined as the width of the dye band on the top roll to that on the bottom roll, as a function of the speed ratio, as shown in Figs. 9 and 10. At speed ratios below 3.6, the width ratio is close to 1.0, indicating a two-dimensional flow. The speed ratio at which ribbing occurs is clearly marked by a sudden increase in the width ratio.

Fig. 10.

Relationship between speed ratio and width ratio of tracer.

The width of the dye was widest at the onset of ribbing, and it follows that it gradually decreased as the speed ratio increased. It is thought that the ribbing wavelength had a low frequency at the onset of ribbing, and a wave of wide wavelength was generated in the width direction and was transferred to a high frequency with increasing roll speed.

3.4. Comparison of Ribbing Generation in Single and Multilayer Coating

The speed ratio of ribbing generation in reverse roll coating was the focus of this experiment, with the aim of determining the existence of a mixture in the meniscus region when the two-layer coating passed over the meniscus region in the two-layer state. First, the speed ratios of ribbing generation in the single-layer condition and two-layer condition were compared. The bottom roll speed was kept constant at 30 mpm. The results are shown in Fig. 11. The critical speed ratio decreases as the liquid viscosity increases. At a liquid viscosity of 5×10^–3 Pa·s, the maximum top roll speed for uniform coating was approximately 120 mpm (V_top/V_bottom=4.0), which decreased to approximately 60 mpm (V_top/V_bottom=2.0) as the liquid viscosity was raised to 20×10^–3 Pa·s. The practical outcome of this result is that high viscosity liquids cannot be coated at high web speeds. In the two-layer condition, the speed ratio of ribbing generation was confirmed by the three differential wet thickness ratio of each layer. In the two-layer condition, the speed ratio of ribbing generation was about 3.5 and expanded greatly in each condition compared with the single-layer 20×10^–3 Pa·s condition.

Fig. 11.

Comparison of ribbing in single and two layer coating. (top layer 20×10^–3 Pa·s, bottom layer 5×10^–3 Pa·s).

On the other hand, in the two-layer condition, the speed ratio of ribbing generation was equal to the case of a liquid viscosity of 20×10^–3 Pa·s in the single-layer condition. Figure 12 shows the results of a comparison with the single-layer condition, where the viscosities of the top and bottom layers are 5×10^–3 Pa·s and 20×10^–3 Pa·s, respectively. The main conclusions from these results are that the onset of ribbing in two-layer coating is not a function of the thickness ratio and is mainly determined by the bottom layer viscosity.

Fig. 12.

Comparison of ribbing in single and two layer coating. (top layer 5×10^–3 Pa·s, bottom layer 20×10^–3 Pa·s).

Next, the internal flow of the meniscus region is considered based on the comparison of the ribbing generation limit speeds. Figure 13 shows the relationship between the viscosity of the coating liquid and the ribbing generation limit speed in the single-layer condition. The generation limit speed of ribbing decreased with increasing viscosity. In the two-layer condition, when the wet thickness ratio was (1) h_top/H=0.4, h_bottom/H=0.4, (2) h_top/H=0.2, h_bottom/H=0.6 and (3) h_top/H=0.6, h_bottom/H=0.2, assuming both layers have mixed completely, the viscosity of the liquid became 9.3×10^–3 Pa·s, 7.4×10^–3 Pa·s, 14.7×10^–3 Pa·s, respectively, and the corresponding ribbing limit speeds would be 2.6, 3 and 2.1. However, in this experiment, these ribbing limit speeds were 3.47, 3.5 and 3.42.

Fig. 13.

Relationship between viscosity and speed ratio.

These values were higher than in the case of a completed mixing condition. Thus, it is thought that complete mixing has not occurred between the two layers in the meniscus region.

Many experimental and theoretical studies have examined the mechanism responsible for generation of ribbing in the single-layer condition. For example, the relationship between meniscus instability and ribbing was discussed by Coyle.²⁾ The equation of ribbing can be expressed as Eq. (1).   

$$\frac{dp}{dx}=\frac{\sigma }{r^2}\frac{dr}{dx}+n^2\sigma$$(1)

n²σ is the term of an additional stabilizing effect. In other words, due to disturbance suppression by surface tension, ribbing does not occur. However, when the disturbance cannot be controlled by surface tension, n²σ is influenced in order to keep a steady flow state. This term influences the ribbing shape. The pressure gradient is the important factor for the ribbing generation.

As for the pressure distribution in the meniscus region, theoretical investigations using a lubrication model and viscocapillary model were carried out by Carvalho and Scrieven⁴⁾ in the case of forward roll coating and T. J. Anderthon¹¹⁾ in the case of reverse roll coating using a deformable roll, a negative gap condition, dimensionless equation systems and boundary conditions were given by Eqs. (2), (3), (4), (5), (6), (7), (8), (9), (10).   

$$\frac{dp}{dx}=Ne\left[\frac{6\left(s+1\right)}{{\left[h\left(x\right)\right]}^2}-\frac{24q}{{\left[h\left(x\right)\right]}^3}\right]$$(2)

  

$$h\left(x\right)=-2+x^2+d\left(x\right)$$(3)

  

$$Ne=\left(\frac{\mu V_B}{ER}\right)\left(\frac{L}{R}\right){\left(\frac{R}{H_0}\right)}^{5/2}$$(4)

  

$$p\left(x_u\right)=-\frac{Ne}{Ca{\left(R/H_0\right)}^{1/2}{r}_u}$$(5)

  

$$p\left(x_d\right)=-\frac{Ne}{Ca{\left(R/H_0\right)}^{1/2}{r}_d}$$(6)

  

$$d\left(x\right)=p\left(x\right)$$(7)

  

$$x_u=-{\left[h_{1\infty }+1.6442\frac{\left(h_1-2q\right)}{\left|s\right|}+r_u\left\{1+\frac{1}{{\left(1+0.863{\left(Ca\left|s\right|\right)}^{2/3}\right)}^{1/2}}\right\}+2-d\left(x_u\right)\right]}^{1/2}$$(8)

  

$$x_d={\left[3.2884q+r_d\left\{1+\frac{1}{{\left(1+0.863{\left(Ca\right)}^{2/3}\right)}^{1/2}}\right\}+2-d\left(x_d\right)\right]}^{1/2}$$(9)

  

$$\frac{x_i-x_{i+1}}{x_1-x_{n+1}}=K$$(10)

where $K=\frac{x_1-x_{n+1}}{n}$

The pressure distribution of the meniscus region was calculated by the matrix method. Figure 14 shows one example of a simulation result in case of the ribbing condition. This result shows that a negative pressure gradient was generated downstream of the meniscus region, substantiating the fact that the generation of ribbing was the downstream of the meniscus region. In other words, in two-layer coating, the limit generation speed ratio of ribbing depends on the viscosity of the lower layer coating if there is no mixing between the two-layers because the lower layer is affected by the downstream side of the meniscus region.

Fig. 14.

Pressure distribution of meniscus region (single layer condision).

In this experimental result, in the two-layer condition, the limit speed ratio of ribbing generation depends on the viscosity condition of the lower layer, and it is thought that the tendency in the numerical analysis substantially corresponds to that of the experiment.

From this result, it is also thought that the mixing does not occur, although a small vortex existed in the meniscus region. However, in the two-layer condition, ribbing is generated when the limit speed ratio of ribbing generation was 3.5. Considering the fact that this limit speed ratio is less than that in the single layer condition, it is possible that mixture occurs between the two layers in a micro-region of the meniscus under high-speed coating conditions.

4. Conclusion

The liquid film surface as it is transferred from a rigid steel roll to a deformable urethane-covered roll was investigated in order to determine how the uniformity of two-layer coating is affected by the speed ratio between two rolls, the wet thicknesses of the layers and the viscosities of the liquids. The conclusions are summarized as follows.

(1) The uniform coating region could be arranged by using the ratio of the wet thickness and slot gap, and the condition for uniform coating was clarified.

(2) The uniform coating region is narrowed by increasing the viscosity of the top layer liquid.

(3) Reverse roll transfer of a two-layer film was analyzed by flow visualization. The results showed the presence of a recirculation in the meniscus, and this recirculation decreases in size and eventually vanished with increasing roll speed.

(4) Liquid transfer is uniform before ribbing generation, and after ribbing generation, the liquid spreads to the width direction along the jaggedness of the ribbing.

(5) The results show that, in two-layer coating, as in single-layer reverse transfer coating, there is a critical web speed above which ribbing occurs. The critical speed is determined by the viscosity of the bottom layer.

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